Tooth movement measurement by automatic impression matching

ABSTRACT

The present invention relates to systems and methods for detecting deviations from an orthodontic treatment plan. One method includes receiving a tracking model, performing a matching step between individual teeth in a plan model and the tracking model, comparing the tracking model with the plan model, and detecting one or more positional differences.

BACKGROUND OF THE INVENTION

The present invention relates generally to the field of orthodontics,and more particularly to a system and method for detecting positionaldifferences between different models of a patient's teeth, as well asdeviations from a planned course of treatment to gradually repositionteeth.

An objective of orthodontics is to move a patient's teeth to positionswhere function and/or aesthetics are optimized. Traditionally,appliances such as braces are applied to the patient's teeth by anorthodontist or dentist and the set of braces exerts continual force onthe teeth and gradually urges them toward their intended positions. Overtime and with a series of clinical visits and adjustments to the braces,the orthodontist adjusts the appliances to move the teeth toward theirfinal destination.

More recently, alternatives to conventional orthodontic treatment withtraditional affixed appliances (e.g., braces) have become available. Forexample, systems including a series of preformed aligners have becomecommercially available from Align Technology, Inc., Santa Clara, Calif.,under the tradename Invisalign® System. The Invisalign® System includesdesigning and/or fabricating multiple, and sometimes all, of thealigners to be worn by the patient before the aligners are administeredto the patient and used to reposition the teeth (e.g., at the outset oftreatment). Often, designing and planning a customized treatment for apatient makes use of computer-based 3-dimensional planning/design tools.The design of the aligners can rely on computer modeling of a series ofplanned successive tooth arrangements, and the individual aligners aredesigned to be worn over the teeth and elastically reposition the teethto each of the planned tooth arrangements.

While patient treatment and tooth movements can be plannedprospectively, in some cases orthodontic treatment can deviate from theplanned treatment or stages. Deviations can arise for numerous reasons,and can include biological variations, poor patient compliance, and/orfactors related to biomechanical design. In the case of aligners,continued treatment with previously designed and/or fabricated alignerscan be difficult or impossible where a patient's teeth deviatesubstantially from the planned treatment course. For example, subsequentaligners may no longer fit the patient's teeth once treatmentprogression has deviated from the planned course.

Because detecting a deviation from planned treatment most typicallyrelies on visual inspection of the patient's teeth or observation ofappliances no longer fitting, treatment can sometimes progresssignificantly off track by the time a deviation is detected, therebymaking any required corrective measures more difficult and/orsubstantial. Earlier and better off track determinations would,therefore, be beneficial in order to recalibrate the fit of the alignerdevice on the teeth. Accordingly, improved methods and techniques ofdetecting and correcting treatment that has deviated from planned ordesired treatment course would be desirable, particularly methodsallowing early detection of treatment deviation.

BRIEF SUMMARY OF THE INVENTION

The present invention provides improved systems and methods detectingpositional differences between different models of a patient's teeth.Such methods and systems can include automatic detection of deviationsfrom an orthodontic treatment plan, tracking a patient's progressaccording to a planned treatment, and can further include incorporatingenhanced tracking techniques into treatment delivery and management. Ifnecessary, revising or modifying the patient's treatment plan based on adetermination that treatment has progress off track can be accomplished.Information obtained according to the invention techniques can be used,for example, to more actively and/or effectively manage delivery oforthodontic treatment, increasing treatment efficacy and successfulprogression to the patient's teeth to the desired finished positions.

Thus, in one aspect, the present invention includes systems and methodsfor detecting deviations from an orthodontic treatment plan. A methodcan include, for example, receiving a tracking model comprising adigital representation of an actual arrangement of a patient's teethafter an orthodontic treatment plan has begun for the patient;performing a matching step between individual teeth in a plan model andthe tracking model; comparing the tracking model with the plan model;and detecting one or more positional differences between the actualarrangement of the patient's teeth and the pre-determined plannedarrangement of the patient's teeth.

The present invention further includes systems and methods for managingdelivery and patient progression through an orthodontic treatment plan.Such a method can include, for example, providing an initial treatmentplan for a patient; providing a plurality of orthodontic appliances; andtracking progression of the patient's teeth along the treatment path.

A method and system according to another embodiment of the presentinvention can include receiving a tracking model comprising a digitalrepresentation of an actual arrangement of a patient's teeth after anorthodontic treatment plan has begun for the patient for comparison to aplan model (e.g., including a pre-determined planned arrangement of thepatient's teeth); performing an alignment step between the plan modeland the tracking model using partial regions beyond a tooth crown ofeach of the plan model and the tracking model such that stationaryelements of each of the plan model and the tracking model are alignedwith one another; and detecting one or more positional differencesbetween the actual arrangement of the patient's teeth and thepre-determined planned arrangement of the patient's teeth.

For a fuller understanding of the nature and advantages of the presentinvention, reference should be made to the ensuing detailed descriptionand accompanying drawings. Other aspects, objects and advantages of theinvention will be apparent from the drawings and detailed descriptionthat follows.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing the anatomical relationship of the jaws of apatient.

FIG. 2A illustrates in more detail the patient's lower jaw and providesa general indication of how teeth may be moved according to anembodiment of the present invention.

FIG. 2B illustrates a single tooth from FIG. 2A and definesdetermination of tooth movement distance according to an embodiment ofthe present invention.

FIG. 2C illustrates the jaw of FIG. 2A together with an incrementalpositioning adjustment appliance according to an embodiment of thepresent invention.

FIG. 3 shows generating and administering treatment according to anembodiment of the present invention.

FIG. 4 illustrates generating a treatment plan according to anembodiment of the present invention.

FIG. 5 illustrates a process including teeth matching according to oneembodiment of the present invention.

FIG. 6 illustrates a data structure according to an embodiment of thepresent invention.

FIG. 7 illustrates a matching range for different teeth according to anembodiment of the present invention.

FIG. 8 illustrates a spatial reference diagram for “point to plane”calculations according to an embodiment of the present invention.

FIG. 9 illustrates a process for rough matching according to anembodiment of the present invention.

FIG. 10 illustrates a model for jaw patch detection according to anembodiment of the present invention.

FIG. 11 illustrates a model for which a jaw patch has been detectedaccording to an embodiment of the present invention.

FIG. 12 illustrates a spatial representation for calculating FHDaccording to an embodiment of the present invention.

FIG. 13A illustrates a tracking model for which buccal ridge points havebeen detected according to an embodiment of the present invention.

FIG. 13B illustrates a planning model for which buccal ridge points havebeen detected according to an embodiment of the present invention.

FIG. 14 illustrates a model for which an AMPB has been generatedaccording to an embodiment of the present invention.

FIG. 15 illustrates a tooth and associated movement vertices accordingto an embodiment of the present invention.

FIG. 16 illustrates a model for which an archform has been constructedaccording to an embodiment of the present invention.

FIG. 17 illustrates a model for which an archform basis for a crowncenter has been constructed according to an embodiment of the presentinvention.

FIG. 18 illustrates an XML output according to an embodiment of thepresent invention.

FIG. 19 shows a process including teeth matching according to anotherembodiment of the present invention.

FIG. 20 illustrates a model for detecting partial regions according toan embodiment of the present invention.

FIG. 21 illustrates a histogram of the matching ratio for all teethaccording to an embodiment of the present invention.

FIG. 22A illustrates a histogram of the number of teeth having matchingratios for individual teeth in an upper jaw according to an embodimentof the present invention.

FIG. 22B illustrates a histogram of the number of teeth having matchingratios for individual teeth in a lower jaw according to an embodiment ofthe present invention.

FIG. 23A shows a graph of the mesial-distal movement distribution of theroot centers of molars according to an embodiment of the presentinvention.

FIG. 23B shows a graph of the mesial-distal movement distribution of thecrown centers of molars according to an embodiment of the presentinvention.

FIG. 24A through FIG. 24C show plurality of stages of teeth correctionand revision of treatment, according to several embodiments of thepresent invention.

FIG. 25 is a block diagram illustrating a system for generatingappliances in accordance with methods and processes of the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION

The present application is directed to subject matter related to U.S.application Ser. No. 11/760,689, entitled “Systems And Method ForManagement And Delivery Of Orthodontic Treatment,” filed on Jun. 8,2007; U.S. application Ser. No. 11/760,705, entitled “Treatment ProgressTracking And Recalibration,” filed on Jun. 8, 2007; U.S. applicationSer. No. 11/760,701, entitled “Treatment Planning and Progress TrackingSystems and Methods,” filed on Jun. 8, 2007; and U.S. application Ser.No. 11/760,612 entitled “System And Method For Detecting DeviationsDuring The Course Of An Orthodontic Treatment To Gradually RepositionTeeth,” filed on Jun. 8, 2007.

The invention described herein provides improved and more automatedsystems and methods detecting positional differences between differentmodels of a patient's teeth. The present invention can include trackinga patient's progress according to a planned treatment, incorporatingenhanced tracking techniques into treatment delivery and management,and, if necessary, revising or modifying the patient's treatment planbased on a determination that treatment has progressed off track.Systems and methods of treatment progress tracking and revised planningcan be included in a variety of orthodontic treatment regimens. Forexample, the progress tracking and revised planning features can beoptionally included and incorporated into other aspects of treatmentaccording to the Invisalign® System. Treatment can be pre-planned foradministering to a patient in a series of one or more phases, with eachphase including a set of appliances that are worn successively by thepatient to reposition the teeth through planned arrangements andeventually toward a selected final arrangement. Progress tracking,according to the present invention, is incorporated into the pre-plannedtreatment for monitoring and management, and to provide enhanceddetection and feedback as to whether treatment is progressing on track.

Model comparison and/or tracking steps according to the presentinvention can occur at any point during treatment but will typically bescheduled to correspond with a patient completing a pre-planned phase oftreatment (e.g., wearing each appliance in a designated set). Forexample, once initial staging of a patient's teeth is completed (e.g.,modeling of a patient's initial, intermediate, and final teetharrangements) and a treatment plan has been devised, a dentalpractitioner can be sent a set of one or more appliances to beadministered to the patient in the first phase of treatment. After thelast appliance in the set is administered to the patient, an image ofthe patient's teeth in their positions following administration of thefirst set of appliances can be taken (e.g., using scan techniques,impression techniques, etc.). From the image of the patient's teeth intheir current position, an assessment can be made as to how thetreatment is tracking relative to original treatment projections. Ifthere is a substantial deviation from the planned treatment path, thencorrective action can be taken, for example, in order to achieve theoriginal designed final position. Treatment then progresses to the nextphase, where either the treatment can be finalized if the intended finalpositions are reached, or a subsequent set of appliances can be sent tothe practitioner for administration to the patient. The subsequent setof appliances can be based on the initial treatment plan if treatment isprogressing on track, or can be based on a revised or modified treatmentplan when a determination is made that treatment is off track.

Methods and techniques for comparing tooth models for positionaldifferences of the teeth and/or tracking tooth movement progress througha planned treatment are generally referred to herein as “teeth matching”or “bite matching.” For example, comparison or matching techniquesdescribed herein can include matching teeth from the a model of thepatient's teeth that may have been used for treatment planning orstaging incremental movements of the patient's teeth according to aplanned orthodontic treatment, to a new model of the teeth taken aftertreatment has begun. An off-track determination can be followed by“re-setting” to the actual position of the teeth as defined by datarepresented in the progress scan, the original data of the teeth (i.e.,segmented models from initial treatment plan), thereby allowingpreservation of the initially selected final target position of theteeth. In other words, the original data set, which contains with it anestablished target arrangement, can be reused by repositioning the teetharrangement according to the positions of the (same) teeth captured inthe progress scan. In so doing, a new planned path to go from thecurrent teeth arrangement to the target teeth arrangement can berecreated without having to change the originally established targetarrangement.

Comparison and matching according to the present invention can includeusing automatic alignment and matching techniques including severalgeneral steps. According to such teeth matching techniques, a trackingmodel or progress scan model is automatically aligned to a plan model,and teeth of the two models are matched. This step allows finding eachtooth's position in the tracking model. Next, stationary andnear-stationary teeth are detected, e.g., either by analysis of theplanned teeth movements, or by statistical analysis. The result caninclude a set of stationary references for computing of teeth movements.Next, the measurement references (e.g., archform and occlusal plan) canbe built from the plan model, and the planned and achieved toothmovement can be measured with respect to those references. Using suchteeth matching techniques provides significant advantages in terms ofmore automation and efficiency as there is no need to re-segment andprocess the new scan of the teeth, and in terms of efficacy in overalltreatment since the initial final arrangement is preserved, even if thepatient progresses off track.

Incorporating the inventive techniques and tracking methods describedherein in managing delivery/modification would provide variousadvantages, including earlier detection of treatment deviations,allowing earlier remedial measures to be taken, if necessary, to avoidundesirable treatment outcomes and preservation of initial treatmentgoals, thereby ultimately allowing for more effective treatment andbetter clinical outcomes. Furthermore, treatment efficiency and efficacycan be increased by better avoidance of inefficient and/or undesirabletreatment “detours.” Additionally, improved monitoring and tracking, asdescribed, is more objective and reliable, and less qualitative innature than the common practice of visually identifying off-trackprogress. This reduces the inter-clinician variability and reduces thedependency of accurate detection on clinician experience. As such,currently described inventive methods and techniques can inspire moreconfidence in both patients and practitioners, including practitionersthat may be less experienced with a given treatment method and/or lessconfident in their abilities to clinically detect off-track progression,or even more experienced practitioners who desire more detailedmonitoring, for example, in cases involving more difficult and/or lesspredictable movements.

FIG. 1 shows a skull 10 with an upperjaw bone 22 and a lowerjaw bone 20.The lowerjaw bone 20 hinges at a joint 30 to the skull 10. The joint 30is called a temporal mandibular joint (TMJ). The upperjaw bone 22 isassociated with an upper jaw 101, while the lower jaw bone 20 isassociated with a lowerjaw 100. A computer model of the jaws 100 and 101is generated, and a computer simulation models interactions among theteeth on the jaws 100 and 101. The computer simulation allows the systemto focus on motions involving contacts between teeth mounted on thejaws. The computer simulation allows the system to render realistic jawmovements that are physically correct when the jaws 100 and 101 contacteach other. The model of the jaw places the individual teeth in atreated position. Further, the model can be used to simulate jawmovements including protrusive motions, lateral motions, and “toothguided” motions where the path of the lower jaw 100 is guided by teethcontacts rather than by anatomical limits of the jaws 100 and 101.Motions are applied to one jaw, but may also be applied to both jaws.Based on the occlusion determination, the final position of the teethcan be ascertained.

Referring now to FIG. 2A, the lower jaw 100 includes a plurality ofteeth 102. At least some of these teeth may be moved from an initialtooth arrangement to a final tooth arrangement. As a frame of referencedescribing how a tooth may be moved, an arbitrary centerline (CL) may bedrawn through the tooth 102. With reference to this centerline (CL),each tooth may-be moved in orthogonal directions represented by axes104, 106, and 108 (where 104 is the centerline). The centerline may berotated about the axis 108 (root angulation) and the axis 104 (torque)as indicated by arrows 110 and 112, respectively. Additionally, thetooth may be rotated about the centerline, as represented by an arrow112. Thus, all possible free-form motions of the tooth can be performed.

FIG. 2B shows how the magnitude of any tooth movement may be defined interms of a maximum linear translation of any point P on a tooth 102.Each point (e.g., P1 and P2) will undergo a cumulative translation asthat tooth is moved in any of the orthogonal or rotational directionsdefined in FIG. 2A. That is, while the point will usually follow anonlinear path, there is a linear distance between any point in thetooth when determined at any two times during the treatment. Thus, anarbitrary point P1 may in fact undergo a true side-to-side translationas indicated by arrow d1, while a second arbitrary point P2 may travelalong a path including one or more than one curves or acute angles orthe like, resulting in a final translation d2. Many aspects of thepresent invention are defined in terms of the maximum permissiblemovement of a point P1 induced on any particular tooth. Such maximumtooth movement, in turn, is defined as the maximum linear translation ofthat point P1 on the tooth that undergoes the maximum movement for thattooth in any treatment step.

FIG. 2C shows one adjustment appliance 111 which is worn by the patientin order to achieve an incremental repositioning of individual teeth inthe jaw as described generally above. The appliance can include a shell(e.g., polymeric shell) having teeth-receiving cavities that receive andresiliently reposition the teeth. Such appliances, including thoseutilized in the Invisalign® System, as well as treatment planningaspects, are described in numerous patents and patent applicationsassigned to Align Technology, Inc. including, for example in U.S. Pat.Nos. 6,450,807, and 5,975,893, as well as on the company's website,which is accessible on the World Wide Web (see, e.g., the url“align.com”).

As set forth in the prior applications, each appliance may be configuredso that its tooth-receiving cavity has a geometry corresponding to anintermediate or final tooth arrangement intended for the appliance. Thepatient's teeth are progressively repositioned from their initial tootharrangement to a final tooth arrangement by placing a series ofincremental position adjustment appliances over the patient's teeth. Theadjustment appliances can be generated all at the same stage or in setsor batches, e.g., at the beginning of a stage of the treatment, and thepatient wears each appliance until the pressure of each appliance on theteeth can no longer be felt or has resulted in the maximum allowabletooth movement for that given stage. A plurality of different appliances(e.g., a set) can be designed and even fabricated prior to the patientwearing any appliance of the plurality. At that point, the patientreplaces the current appliance with the next appliance in the seriesuntil no more appliances remain. The appliances are generally notaffixed to the teeth and the patient may place and replace theappliances at any time during the procedure. The final appliance orseveral appliances in the series may have a geometry or geometriesselected to overcorrect the tooth arrangement, i.e., have a geometrywhich would (if fully achieved) move individual teeth beyond the tootharrangement which has been selected as the “final.” Such over-correctionmay be desirable in order to offset potential relapse after therepositioning method has been terminated, i.e., to permit movement ofindividual teeth back toward their pre-corrected positions.Over-correction may also be beneficial to speed the rate of correction,i.e., by having an appliance with a geometry that is positioned beyond adesired intermediate or final position, the individual teeth will beshifted toward the position at a greater rate. In such cases, the use ofan appliance can be terminated before the teeth reach the positionsdefined by the appliance.

Referring to FIG. 3, a method 200 according to the present invention isillustrated. Individual aspects of the process are discussed in furtherdetail below. The process includes generating a treatment plan forrepositioning a patient's teeth (Step 202). Briefly, a treatment planwill include obtaining data comprising an initial arrangement of thepatient's teeth, which typically includes obtaining an impression orscan of the patient's teeth prior to the onset of treatment. Thetreatment plan will also include identifying a final or targetarrangement of the patient's teeth that is desired, as well as aplurality of planned successive or intermediary tooth arrangements formoving the teeth along a treatment path from the initial arrangementtoward the selected final or target arrangement. Appliances can begenerated based on the planned arrangements and administered to thepatient (Step 204). The appliances are typically administered in sets orbatches of appliances, such as sets of 2, 3, 4, 5, 6, 7, 8, 9, or moreappliances, but are not limited to any particular administrative scheme.After the treatment plan begins and following administration ofappliances to the patient, teeth matching is done to assess a currentand actual arrangement of the patient's teeth compared to a plannedarrangement (Step 206). If the patient's teeth are determined to be“on-track” and progressing according to the treatment plan (e.g., thepatient's teeth are moving at a rate and/or in accordance with thetreatment plan), then treatment progresses as planned. If the patient'steeth have reached the initially planned final arrangement, thentreatment progresses to the final stages of treatment (Step 208). Wherethe patient's teeth are determined to be tracking according to thetreatment plan, but have not yet reached the final arrangement, the nextset of appliances can be administered to the patient (repeat Step 204,according to the initial treatment plan). If, on the other hand, thepatient's teeth are determined at the teeth matching step (Step 206) notto be tracking with the treatment plan (e.g., the patient's teeth arenot moving at a rate and/or in accordance with the treatment plan), thentreatment is characterized as “off-track” and an assessment is made asto how further treatment of the patient will proceed. Typically, arevised treatment plan will be generated (Step 210), and may beselected, for example, to reposition the teeth from the current positionto a final position, which may be the same destination as the initiallydetermined final position according to the initial treatment plan.

Systems of the present invention can include network based systems,including a data network and a server terminal operatively coupled tothe network. One or more client terminals can be included andoperatively coupled to the network. Systems can optionally include morestand-alone or non-network based systems, including computers andsoftware packages designed to at least partially operate independent ofa data network and in which various steps of the currently describedmethods can be accomplished in an automated fashion at a remote location(e.g., practitioner's office).

FIG. 4 illustrates the general flow of an exemplary process 300 fordefining and generating a treatment plan, including repositioningappliances for orthodontic treatment of a patient. The process 300includes the methods, and is suitable for the apparatus, of the presentinvention, as will be described. The steps of the process can beimplemented as computer program modules for execution on one or morecomputer systems.

As an initial step, a mold or a scan of patient's teeth or mouth tissueis acquired (Step 302). This generally involves taking casts of thepatient's teeth and gums, and may in addition or alternately involvetaking wax bites, direct contact scanning, x-ray imaging, tomographicimaging, sonographic imaging, and other techniques for obtaininginformation about the position and structure of the teeth, jaws, gumsand other orthodontically relevant tissue. From the data so obtained, adigital data set is derived that represents an initial (e.g.,pretreatment) arrangement of the patient's teeth and other tissues.

The initial digital data set, which may include both raw data fromscanning operations and data representing surface models derived fromthe raw data, is processed to segment the tissue constituents from eachother (Step 304), including defining discrete dental objects. Forexample, data structures that digitally represent individual toothcrowns can be produced. In some embodiments, digital models of entireteeth are produced, including measured or extrapolated hidden surfacesand root structures.

Desired final position of the teeth, or tooth positions that are adesired and/or intended end result of orthodontic treatment, can bereceived, e.g., from a clinician in the form of a descriptiveprescription, can be calculated using basic orthodontic prescriptions,or can be extrapolated computationally from a clinical prescription(Step 306). With a specification of the desired final positions of theteeth and a digital representation of the teeth themselves, the finalposition and surface geometry of each tooth can be specified (Step 308)to form a complete model of the teeth at the desired end of treatment.The result of this step is a set of digital data structures thatrepresents a desired and/or orthodontically correct repositioning of themodeled teeth relative to presumed-stable tissue. The teeth andsurrounding tissue are both represented as digital data.

Having both a beginning position and a final target position for eachtooth, the process next defines a treatment path or tooth path for themotion of each tooth (Step 310). This includes defining a plurality ofplanned successive tooth arrangements for moving teeth along a treatmentpath from an initial arrangement to a selected final arrangement. In oneembodiment, the tooth paths are optimized in the aggregate so that theteeth are moved in the most efficient and clinically acceptable fashionto bring the teeth from their initial positions to their desired finalpositions.

At various stages of the process, the process can include interactionwith a clinician responsible for the treatment of the patient (Step312). Clinician interaction can be implemented using a client processprogrammed to receive tooth positions and models, as well as pathinformation from a server computer or process in which other steps ofprocess 300 are implemented. The client process is advantageouslyprogrammed to allow the clinician to display an animation of thepositions and paths and to allow the clinician to reset the finalpositions of one or more of the teeth and to specify constraints to beapplied to the segmented paths.

The tooth paths and associated tooth position data are used to calculateclinically acceptable appliance configurations (or successive changes inappliance configuration) that will move the teeth on the definedtreatment path in the steps specified (Step 314). Each applianceconfiguration corresponds to a planned successive arrangement of theteeth, and represents a step along the treatment path for the patient.The steps are defined and calculated so that each discrete position canfollow by straight-line tooth movement or simple rotation from the toothpositions achieved by the preceding discrete step and so that the amountof repositioning required at each step involves an orthodonticallyoptimal amount of force on the patient's dentition. As with other steps,this calculation step can include interactions with the clinician (Step312).

Having calculated appliance definitions, the process 300 can proceed tothe manufacturing step (Step 316) in which appliances defined by theprocess are manufactured, or electronic or printed information isproduced that can be used by a manual or automated process to defineappliance configurations or changes to appliance configurations.Appliances according to the treatment plan can be produced in entirety,such that each of the appliances are manufactured (e.g., prior totreatment), or can be manufactured in sets or batches. For example, insome cases it might be appropriate to manufacture an initial set ofappliances at the outset of treatment with the intention ofmanufacturing additional sets of appliances (e.g., second, third,fourth, etc.) after treatment has begun (e.g., as discussed furtherherein). For example, a first set of appliances can be manufactured andadministered to a patient. Following administration, it may be desirableto track the progression of the patient's teeth along the treatment pathbefore manufacturing and/or administering subsequent set(s) ofappliances.

Generating and/or analyzing treatment plans, as discussed herein, caninclude, for example, use of 3-dimensional orthodontic treatmentplanning tools such as Treat® from Align Technology, Inc. or othersoftware available from eModels and OrthoCAD, among others. Thesetechnologies allow the clinician to use the actual patient's dentitionas a starting point for customizing the treatment plan. The Treat®technology uses a patient-specific digital model to plot a treatmentplan, and then use a scan of the achieved or actual treatment outcome toassess the degree of success of the outcome as compared to the originaldigital treatment plan as discussed in U.S. patent application Ser. No.10/640,439, filed Aug. 21, 2003 and U.S. patent application Ser. No.10/225,889 filed Aug. 22, 2002. (see also, below).

In some cases, patients do not progress through treatment as expectedand/or planned. For example, in some instances a patient's progressionalong a treatment path can become “off-track” or will deviate from aninitial treatment plan, whereby an actual tooth arrangement achieved bythe patient will differ from the expected or planned tooth arrangement,such as a planned tooth arrangement corresponding to the shape of aparticular appliance. A determination that the progression of apatient's teeth is deviating or not tracking with the original treatmentplan can be accomplished in a variety of ways. As set forth above,off-track deviations can be detected by visual and/or clinicalinspection of the patient's teeth. For example, a substantial off trackdeviation from the expected or planned treatment may become apparentwhen the patient tries to wear a next appliance in a series. If theactual tooth arrangement substantially differs from the plannedarrangement of the teeth, the next appliance will typically not be ableto seat properly over the patient's teeth. Thus, an off-track deviationmay become substantially visually apparent to a treating professional,or even to the patient, upon visual or clinical inspection of the teeth.

Detecting deviations from a planned treatment, however, can bedifficult, particularly for patients as well as certain dentalpractitioners, such as those with more limited experience inorthodontics, certain general dentists, technicians, and the like.Additionally, deviations that have progressed to the point that they arevisually detectable clinically are often substantially off track withrespect to the planned treatment, and earlier means of off-trackdetection is often desired. Thus, detecting deviations from a treatmentplan can also be accomplished by comparing digital models of thepatients teeth, and can often detect deviations from a treatment planbefore the deviation becomes substantially apparent by visual orclinical inspection, advantageously resulting in reduced costs,treatment plan times and patient discomfort.

One exemplary known computer based teeth matching process includescomparing an actual position of the teeth relative to a planned orexpected position using comparison of two processed or segmented scansof the patient's teeth—a processed plan treatment and a processed (e.g.,segmented) tracking model. See, e.g., commonly owned U.S. Pat. Nos.7,156,661 and 7,077,647 for discussion of comparing actual positions ofthe teeth relative to a planned or expected position using a processed(e.g., segmented) scan of the teeth positions following initiation oftreatment.

Another exemplary computer based teeth matching process includescomparing a previously segmented planned model of the patient's teeth toan unsegmented or non-segmented representation of an actual arrangementof the patient's teeth, or tracking model, that has been furtherprocessed including marking of Facial Axis of the Clinical Crown (FACC)for each teeth in the tracking model. See, e.g., commonly owed U.S.application Ser. No. 11/760,612, entitled “System and Method forDetecting Deviations During the Course of an Orthodontic Treatment toGradually Reposition Teeth,” filed Jun. 8, 2007, for further discussionof comparing a non-segmented, FACC marked, representation of an actualarrangement of a patient's teeth after treatment has begun to apreviously segmented model of the patient's teeth.

The present invention includes automatic alignment and matching systemsand methods of measuring and evaluating tooth movements based onmatching a patient's impression model or tracking model obtained duringtreatment or after tooth movement treatment has begun, with a plan modelfrom treatment planning. By automatic alignment and matching of thetracking model and the plan model, a planned tooth movement and actuallyachieved tooth movement during a stage of treatment can be compared andevaluated.

Automatic alignment and matching according to the present inventionincludes several general steps. First, a tracking model is automaticallyaligned to a plan model, and teeth of the two models are matched. Thisstep allows finding each tooth's position in the tracking model. Second,stationary and near-stationary teeth are detected, e.g., either byanalysis of the planned teeth movements, or by statistical analysis. Theresult can include a set of stationary references for computing of teethmovements. Third, the measurement references (e.g., archform andocclusal plane) can be built from the plan model, and the planned andachieved tooth movement can be measured with respect to thosereferences. Such planned and achieved tooth movement measurementsconstitute valuable information which, as mentioned, can be used fortreatment progress tracking, monitoring, and calibration, as well asorthodontic/biology study and research, tooth movement velocity study,appliance performance analysis, and the like.

An exemplary method of automatic alignment and matching of a trackingmodel and treatment plan model according to the present invention isdescribed with reference to FIG. 5. As shown, FIG. 5 illustrates thegeneral flow of an exemplary process 400 for detecting deviations from aplanned treatment. Steps of the process 400 can be implemented by acomputer based system, such as computer program modules for execution onone or more computer systems.

As an initial step, a tracking model and one or more planning models ofthe patient's teeth are obtained as described further herein and canthen be received by or loaded into a system for automatic alignment andmatching according to techniques of the present invention (Step 402).The tracking model is a three-dimensional digital model, i.e. a digitalrepresentation, of a patient's teeth during treatment. The trackingmodel may be acquired by various methods, including scanning thepatient's teeth or impressions of the patient's teeth, or via any otherdirect or indirect method of acquiring a three-dimensional digital modelof a patient's teeth, such as 3D laser scanning, 3D CT scanning,stereophotogrammetry, intra-oral direct dental scanning, and destructivescanning techniques. The one or more plan models are three-dimensionaldigital models of desired and/or actual teeth arrangements in accordancewith the treatment plan as described above (see, e.g., FIG. 4). Forexample, the one or more plan models (e.g., segmented models) mayinclude a digital model of the patient's initial teeth arrangement, aplanned intermediate arrangement of the patient's teeth, and/or aplanned target or final arrangement of the patient's teeth. Automaticalignment and matching, according to methods of the present invention,typically includes comparison of an unsegmented tracking model with aplan model that have already been processed and segmented duringtreatment planning stages.

After loading the tracking and one or more plan models, a matching stepis performed between a plan model and the tracking model (Step 404).Matching according to Step 404 can include first performing a roughmatching step where the teeth of models are roughly aligned. Forexample, the teeth of the tracking model can be roughly matched to(i.e., aligned with) the teeth of the plan model. In one embodiment,rough matching can be accomplished by detecting the buccal ridge ellipseof each of the tracking model and the plan model and aligning thedetected buccal ridge ellipses with one another (Step 404A). Followingrough matching, the two models can be fine aligned (i.e., furtheraligned to achieve a closer match between the two models) by theapplication of surface matching algorithms, feature matching algorithms,and the like (Step 404B). 3D model registration algorithms may also beemployed. In an embodiment of the present invention, the “IterativeClosest Point” (ICP) surface matching algorithm is used. Fine alignmentcan include matching the tracking model to a plurality of plan models,e.g., each representing different or progressive stages of a plannedtreatment, so as to find the best match between a particular one of theone or more plan models and the tracking model (Step 404B). Finealignment can further include matching individual teeth of the planmodel with the tracking model (e.g., the plan model found via Step 404Bthat best matches the tracking model) (Step 404C). Such individual teethmatching can also be implemented by applying the “Iterative ClosesPoint” (ICP) algorithm tooth by tooth. As a result of the matching step404, including rough matching, fine alignment and individual teethmatching, each tooth in the plan model can be aligned to correspondingposition in the tracking model. So the positions of the teeth in thetracking model can be found, with the advantage of using only ofnon-segmented tracking model and fully automatic operation without humaninteraction.

Next, the process may include an additional matching (i.e.,re-alignment) step, including comparing the tracking model with the planmodel, so as to detect stationary elements (e.g., stationary teeth) ofthe patient's dentition such that positions of non-stationary teeth canbe measured relative to the detected stationary elements (Step 406).Such a comparison can include comparing or superimposing the trackingmodel with a plan model (any plan model, including the best matchplanning model, may be used). The stationary elements can be teethdetermined as having minimal movement according to the treatment plan oras detected by statistical analysis. Because the teeth positions in thetracking model are known from the matching step described above (Step404), the alignment of the tracking model to the plan model can beaccomplished, in one embodiment, by optimizing the square distance ofall vertices in two models (one in the tracking model, another in theplan model), where the vertices are weighted according to theirprobability of being associated with stationary teeth.

Next, the process can compare planned tooth positions with actuallyachieved tooth positions (Step 408) so as to detect one or morepositional differences between the actual and planned movement of thepatient's teeth. Such a comparison can include building up an occlusalplane and archform as a measurement reference (Step 408A) and computingtooth movements relative to this measurement reference (Step 408B).

Iterative Closest Point Algorithm

As described above, fine matching of two models (Step 404B) and matchingeach tooth of a plan model with tracking model (Step 404C) can includeutilization of a 3D model registration algorithm. One such algorithmthat can find use in the methods of the present invention is an“Iterative Closest Point” (ICP) algorithm.

In general, surface matching (e.g., model registration, model matching,point registration etc.) is a common and challenging problem in manycomputer graphics applications. ICP is an algorithm well suited forsurface matching. The basic idea for utilizing ICP according to thepresent invention is to find closest point pairs between two models, orbetween corresponding teeth in each of two models, assuming that aftermatching every pair should become one point. The points can be, forexample, vertexes located on a surface of a model. The surfaces may besurfaces of the teeth of the model, surfaces of fixed accessories toteeth, surfaces of the gingiva of the model, and the like. Then, thetransformation is computed to minimize the distances between the pairsof points. The general steps of the ICP algorithm are as follows:selecting source points (from at least one or of a model); determiningmatching points on another model by finding points on at least onesurface of the other model (e.g., mesh) that are closest to points onthe at least one surface of the model; rejecting certain point pairs,such as point pairs constituting outlier points; assigning an errormetric to distances between points in pairs; minimizing the error metricby computing a rigid body transform and applying it to one of the modelsand make that model moved to new position. Then, the above steps arerepeated for the moved model: searching new point pairs; assigning newerror metric and computing new transformation by minimizing errormetric. Repeat these steps until the error has converged or maximumiteration number achieved.

According to one embodiment of the present invention, the followingdetailed algorithms can be used. First, a coarse-fine volume (CFV) datastructure can be used to find closest points. The CFV data structure canbe a two level, 3 dimensional array that stores the closest vertex ofeach point in the neighborhood of the model. Advantageously, CFV datastructures are very fast and memory efficient. Second, an adaptivematching range can be used to reject outlier point pairs. The matchingrange is gradually reduced and adapted to the level of noise.Accordingly, the search for closest points encompasses both “coarse tofine point matching” and “reject outlier” features. Third, the distancefrom a point to a fixed plane can be used as the error metric. Fourth,singular value decomposition (SVD) can be used for the rigid bodytransform computation.

CFV Data Structure

The CFV data structure and its use according to the present inventionare further described. Conventionally, a 3D model is represented as setsof vertices and triangular faces. A model may contain numerous (e.g.,thousands, millions, etc.) vertices and triangles. It may take onlyseveral milliseconds to find one pair of points from two models, but itwill take seconds, even minutes to find thousands of pairs. It's evenmore time consuming to apply the ICP algorithm because the ICP algorithmrequires dozens to hundreds of iterations, where each iteration requiresthousands of searches for point pairs.

Different algorithms have developed to speed up this process, likeoctree, k-d tree. The basic idea of these different algorithms is toorganize the scatted vertices in space in such a way that for eachsearch only a small number of comparisons is needed. In one embodimentof the present invention, 3 dimensions space is divided into small cubesand represented by a 3 dimensions array in software program. Eachelement of the array stores the closest vertex from the center of cubeto the model. That means, given a point in 3D, the closest vertex to amodel can be immediately found, which is the only vertex in the cube thepoint is located. However, when only a limited amount of memory isavailable to store points in 3D, a “coarse to fine” approach can beused. The use of a “coarse to fine” approach advantageously reduces thememory requirements for storing points in 3D.

FIG. 6 is a 2D illustration of a CSV 3D data structure 500 in accordancewith an embodiment of the present invention. The data structure 500includes a bounding cube 502 that encompasses all vertices 502 in themodel. The bounding cube can be uniformly divided into many coarse cubes506. Each coarse cube 506 that is near a vertex 502 of model can bedivided into many fine cubes 504. The data structure 500 canadvantageously be a CFV data structure. For each coarse and/or finecube, the vertex that is closest to the centre of the cube is stored.Also, the parent coarse cube also stores the reference to its fine cubeswhich are represented by a 3 dimensions array.

For a given point in 3D, its closest vertex to the model then is theclosest vertex stored in the coarse or fine cube it located. For pointsother than cube centers, there may be error in distance to the closestvertex of the mesh since every cube stores only the closet vertex to itscentre. However, the coarse cube is far from the model, so the error issmall compared to the distance to the vertex. For fine cube, its size issmall enough, so the error is also small compared to the distance. Inour application, i.e. the ICP algorithm, the distance computed isaccurate enough, both for coarse or fine cube.

In accordance with one embodiment of the present invention, the datastructure 500 is built by performing the following steps:

1. Initialize coarse cubes and set a reference to the closest vertex forthese cubes as “NULL”.

2. For each vertex in the model, find the coarse cube it is located andthe neighboring cube(s).

3. If the located cube and neighboring coarse cube(s) has no setreference to a closest vertex, then set the reference to the currentvertex. Else, check whether the new vertex is closer to the cube'scenter. If true, replace the vertex reference by the new vertexreference.

4. For the coarse cube that the vertex located, subdivide it into finecubes (which are also represented as 3 dimensions array), if not donebefore.

5. For each fine cube, check the distance of the cube center to thevertex, replace closest vertex reference if the new vertex is closer.

After the CFV data structure is constructed, it can be used to find theclosest vertex from any given point 3D to the model. Advantageously,using the aforementioned data structure, a maximum of only 2 steps areneeded to find the closest point for a given point in 3D; one step toacquire the reference set for a coarse cube. If there are fine cubeslinked in the coarse volume, a second step is used to acquire the vertexreference by look-up the fine cube where the point is in.

Rejecting Outlier Point Pairs

In general, two 3D models typically are not identical since the scanningof the models can be performed from different positions or at differenttimes; or models may be modified in the later processing procedures. Inaccordance with the present invention, teeth are usually moved duringtreatment, so models acquired at the beginning of the treatment andmodels acquired during the course of treatment are not likely to be thesame. Also, tracking models generally represent raw data and thususually contain data acquirement and scanning errors, extra material andnoise. Accordingly, there is often some part in a model that cannot bematched to another model.

In an embodiment of the present invention, the parts of a model thatcannot be matched to another model can be filtered out. A method forfiltering out such parts is to employ an adaptive matching range. Forexample, for a given pair of points, if the distance between the pair ofpoints is bigger than a predetermined distance (i.e., a matching range),the pair of points is considered to be an outlier point pair andtherefore is not used for calculating the matching transformation. Thematching range can be adaptive to the noise level in each iteration ofICP computation.

An exemplary adaptive matching range according to an embodiment of thepresent invention is defined by the formula:MR _(i) =w·MR _(i-1)+(1−w)·(k·D _(i-1) +R)  (1)

Where: MR_(i) is a new matching range, MR_(i-1) is a the matching rangeof a previous iteration, i is the iteration, w (0<w<1.0) is a shrinkcoefficient, k is an error magnification coefficient, D_(i-1) is acurrent average matching error, and R is a minimum match range, whichhas the same magnitude as the scanning error.

The initial value of the matching range, i.e., MR_(o), is set largeenough so that a large number of vertex pair, like 50% of all vertex inthe model can be selected for the first iteration. Then, the matchingrange is gradually reduced due to the weight w<1.0. When the number ofiterations approaches infinity, the matching range approaches:k·D _(i-1) +R  (2)

Here, D is the residual average matching error. So, even if D=0, thematch range is still not zero, so some point pairs can always beselected. If D is large, then MR is also large. That means, for noisydata, the search range can be relatively large; on the other hand, forclean data, the search range can be relatively small.

FIG. 7 illustrates, in accordance with an embodiment of the presentinvention, a graph 600 showing the changes in the matching range fordifferent teeth, i.e., teeth numbered 18, 19, 22, 23, 24, 26 and 31. Thex-axis of FIG. 7 represents the number of iterations of formula (1). They-axis of FIG. 7 represents the resulting matching range in mm. Thematching ranges for all teeth start at 2 mm and reached different finalvalues, reflecting different levels of noise for each tooth.

Advantageously, by using an adaptive matching range, outlier point pairscan be effectively removed. When an adaptive matching range is used formatching a tracking model with a planning model, scanning errors, noise,and extra material due to attachments and the like can be automaticallyremoved.

Error Metric of a Point Pair

In an embodiment of the present invention, an error metric is assignedto distances between point pairs and minimized for calculating thematching transformation. Conventionally, an error metric is calculatedas the square distance of two points according to the following formula:Err=∥P−Q∥ ²=(P−Q)^(T)(P−Q)  (3)

Where Err is the error metric, P is a first point in a point pair, and Qis a second point in the point pair.

In an embodiment of the present invention, the error metric can becalculated using a “point to plane” distance. FIG. 8 illustrates aspatial reference diagram 700 showing a relationship between P, Q and apoint Q₁. For each vertex (i.e., point) Q in a model; there is a normalvector N assigned to it that is normal to a surface of the model atwhich the vertex Q is located. Alternatively, the normal vector N can beequal to an average of at least some, or even all, vectors that arenormal to model surfaces that neighbor the vertex Q. A plane is thusprovided that intersects vertex Q and is perpendicular to the normalvector N. The error metric, in accordance with the “point to plane”distance, can then be calculated as:Err=∥P−Q∥ ²=(P−Q ₁)^(T)(P−Q ₁)  (4)

Where P is a first point (i.e., vertex) in a point pair, Q is a secondpoint (i.e., vertex) in the point pair, and Q₁ is the projected point ofP into the plane provided that intersects Q and is perpendicular to thenormal vector N.

Computing a Rigid Body Transform by SVD.

In an embodiment of the present invention, a rigid body transform iscomputed and applied to a model. Advantageously, “Singular ValeDecomposition” (SVD) can be used as the rigid body transform. Thefollowing algorithm can be used to compute, via SVD, the rigid-bodytransform:

Assume that all point pairs between two models are found as(P _(i) ,Q _(i)), i=1, 2, . . . N  (5)

Where P_(i) is a point from a first of the two models for point pair i,Q_(i) is a point from a second of the two models for point pair i, and Nis the total number of point pairs. The rigid transformation between theresulting two sets of point can be estimated by minimizing the followingcost function:

$\begin{matrix}{J = {{\sum\limits_{i = I}^{N}{{P_{i} - Q_{i}}}^{2}} = {\sum\limits_{i = I}^{N}{\left( {P_{i} - Q_{i}} \right)^{T}\left( {P_{i} - Q_{i}} \right)}}}} & (6)\end{matrix}$

The rigid transform between two models is:Q _(i) =R·P _(i) +T+ε _(i)  (7)

Where R is a rotation matrix, T is a translation vector, ε_(i) is theerror.

Define

$\begin{matrix}{H = {\sum\limits_{i = 1}^{N}{P_{i}Q_{i}^{T}}}} & (8)\end{matrix}$

If the singular value decomposition of H is H=UΛV^(T), then the rotationmatrix R is R=VU^(T), and the translation vector T is:

$\begin{matrix}{T = {{\overset{\_}{Q} - {R*\overset{\_}{P}}} = {{\frac{1}{N}{\sum\limits_{i = 1}^{N}Q_{i}}} - {R*\frac{1}{N}{\sum\limits_{i = 1}^{N}P_{i}}}}}} & (9)\end{matrix}$

Details of using SVD for computing rigid body transformations as well asadditional algorithms for computing rigid body transformations can befound in D. W. Eggertl, A. Lorusso, R. B. Fisher: “Estimating 3-D rigidbody transformations: a comparison of four major algorithms,” MachineVision and Applications, pp. 272-290, 1997, which is incorporated byreference herein in its entirety.

Matching of Tracking and Planning Models

In accordance with an embodiment of the present invention, a matchingstep 404 is performed between a planning model and the tracking model.The matching step 404 can include rough matching 404A, fine matchingmodels and finding a best match stage 404B, and fine matching individualteeth of models and finding tooth positions 404C. One of the purposes ofthe matching step 404 is to determine the positions of the teeth in theimpression model so that tooth movements can subsequently be determinedbased on these positions.

In an embodiment of the present invention, the previously discussed ICPalgorithm is used to fine match a planning model and a tracking model.The ICP algorithm can be used to match the whole planning model and thetracking model, or be used to match individual teeth of the planningmodel with the tracking model, where teeth are not segmented out. In anyevent, before applying the ICP algorithm, a good initial match betweenthe planning model and the tracking model can advantageously bedetermined; i.e., the planning model and the tracking model can beroughly aligned before the ICP algorithm is applied. This step is called“rough alignment” or “rough matching”. Advantageously, applying a roughmatching step before using the ICP algorithm increases the likelihoodthat minimization aspects of the ICP algorithm actually converge,converge on global minimal, and/or converge without requiring an unduenumber of iterations. More important, fully automatic rough matchingalgorithm can make all process automated, that can greatly reduce humanoperation time and errors.

After the tracking model and a planning model are roughly matched, theICP algorithm can be used to finely match the tracking model and theplanning model. In the case that there is more than one planning model,a plurality of planning models can undergo the rough matching and finematching. The planning model that best matches the tracking model can bedetermined. Once the planning model that best matches the tracking modelis determined, then the ICP algorithm can be used once more to finelymatch the teeth of that planning model and the tracking model. Theposition of the teeth in the tracking model can then computed, and thequality of the tooth matching can be evaluated.

Rough Matching

Conventional methods for performing rough matching include manuallymoving two models to roughly matching positions, or marking the samefeature points in two models with subsequent alignment of these featurepoints. Example of feature points includes the corner point,intersection of two edges, dimple points or so on. Another example offeature points the FA point, which is the center pointer of “Facial Axisof Clinical Crown” (FACC) curve. Both of these conventional methods areheavily dependent on human operation and are not suitable for fullyautomatic data analysis.

Conventional methods for performing rough matching also include methodsthat are not dependent on human operation; i.e., fully automaticmatching. These types of methods may be incorporated and are well suitedfor the present invention. Fully automatic 3D model matching approachesinclude:

1. Feature detection and matching (such as high-curvature points (i.e.,corners), flat plane patches, edges, space curves and the like).

2. Translation invariant 2D image matching, like spin-image and ExtendedGaussian Image (EGI).

FIG. 9 illustrates a method for rough matching 800 in accordance with anembodiment of the present invention. The method for rough matching 800utilizes feature detection, where the detected feature is a buccal ridgeellipse.

In a tracking or planning model, the teeth may or may not be segmentedfrom the jaw. Commonly, teeth will not be segmented from jaw fortracking model. In the case that the teeth are not segmented from thejaw, the jaw patch can be detected (Step 802). The jaw patch is thecontinuous smooth part of buccal side of gums and teeth and can beautomatically detected. Advantageously, based on jaw patch, buccal ridgecan also be automatically detected; i.e., the buccal ridge can bedetected without requiring a user to manipulate the model.

In accordance with an embodiment of the present invention, withreference to FIGS. 9 and 10, the jaw patch can be detected (Step 802)via the following routine:

-   -   1. Compute the middle plane 902 of the model 900, where the        middle plane 902 is the average plane of all vertices in the        model 900.    -   2. Determine the centre Z axis 904 of the model 900, where the        centre Z axis 904 passes through the centre of the model 900 and        is normal to the middle plane 902.    -   3. Mark jaw vertices v, by isolating the vertices v where:        -   a. A distance from v to the centre Z-axis 904 is bigger than            R1 906 and smaller than R2 908, where R1 906 is the radius            from the center Z-axis 904 to an innermost vertex of the            model 900 and R2 908 is the radius from the center Z-axis            904 to an outermost vertex of the model 900.        -   b. A norm to the model 900 at vertex v makes an angle with            the centre Z-axis 904 not less 45 degrees.    -   4. Segment the jaw model into “smooth patches” by following        “region growing” algorithm:        -   a. Assign all “jaw vertices” with a patch number 0, means it            is not checked.        -   b. Select one “jaw vertex” from the jaw model that not            “checked” yet (patch number equals 0). Assign the vertex            with a new patch number bigger than 0. Create a variable            length array to store vertices of the patch (called patch            array), and put this jaw vertex in the array as the first            element.        -   c. Get one vertex from the patch, check all of its neighbor            vertices:            -   i. If the neighbor vertex is already marked (patch                number not equal 0), go to next neighbor vertex.            -   ii. Else if the neighbor vertex is close to current                vertex, i.e., the direction of neighbor vertex is close                to current vertex's direction, it is marked as current                patch number and put into patch array.            -   iii. Else go to next neighbor vertex.        -   d. Repeat (c.) until all vertices in the patch array are            processed.        -   e. Increase the patch number by 1. Repeat (b.), until all            “jaw vertices” in the model are processed.    -   5. Choose the largest patch of the “smooth patches” detected.        Slightly grow it bigger to merge other smaller “smooth patches”    -   6. The merged largest patch is then the “jaw patch”.

FIG. 11 illustrates a model 1000 for which a jaw patch 1002 has beendetected in accordance with the aforementioned routine.

In accordance with an embodiment of the present invention, buccal ridgepoints for the treatment and planning models can be detected (Step 804).In the case that at least one of the models includes teeth not segmentedfrom the jaw, Step 804 follows Step 802. In the case that none of themodels included teeth not segmented from the jaw, Step 802 isunnecessary. For planning model, where teeth are segmented, the buccalridge points can be detected tooth by tooth. The buccal ridge of the jawcan be formed by all the buccal ridge points of all teeth. For trackingmodel, the buccal ridges points are detected against the jaw patch(e.g., as described above). Accordingly, the points on the buccal ridgeare high in the Z-direction and far in the buccal direction (i.e., thebuccal ridge points are located in an uppermost and outermost area ofthe tooth or jaw patch). To identify the points on the buccal ridge, thefar-high distance (FHD) of a point to the Z axis is calculated for eachvertex as:FHD=z+w _(r) ·r  (10)

Where z is the distance along the Z axis, r is the distance to the Zaxis, and w_(r) is the weight of the radial direction. FIG. 12illustrates a spatial representation 1100 of the relationship between z,r and FHD for a point 1102. The value of w_(r) is normally less than 1.0and bigger than 0 and may vary tooth by tooth. For anterior teeth likecanine and incisor, w_(r) can be 0.1 to 0.7. For posterior teeth likepremolar and molar, w_(r) can be 0.4 to 0.8. For tracking model, whereonly jaw patch is used, w_(r) can be 0.2 to 0.8.

The buccal ridge points of a model can then be found as the pointshaving the maximal FHD in each radial cross section of the model. FIG.13A illustrates a tracking model 1200 for which buccal ridge points 1202have been detected. FIG. 13B illustrates a planning model 1210 for whichbuccal ridge points 1212 have been detected.

After the buccal ridge points are found, a buccal ridge ellipse can beformed (Step 806) for the models. The buccal ridge ellipse can be formedby the following algorithm:

-   -   1. Find the occlusal plane from all detected buccal ridge points        by Random Sample Consensus (RANSAC) algorithm, which can find a        plane that fit most detected buccal ridge points.    -   2. Project the buccal ridge points into the occlusal plane to        form a two-dimensional array as:        (x _(i) ,y _(i)), i=1, 2, . . . N  (11)

Where N is the total number of detected buccal ridge points.

-   -   3. Assume the points in the two-dimensional array fit the        following quadratic equation:        a·x ² +b·xy+c·y ² +d·x+e·y+f=0  (12)    -   4. Minimize the error using Singular Value Decomposition (SVD)        and get the parameters a, b, c, d, e, and f    -   5. Check the type of the resulting curve (e.g., ellipse or        hyperbola).    -   6. Find the major axis of the ellipse.

Once the buccal ridge ellipse is formed, an Anterior Middle Point Basis(AMPB) can be generated (Step 808) for the models. The AMPB is definedas follows:

The origin point (O) is at the end of the major axis of the buccal ridgeellipse.

The Z-axis is normal to the occlusal plane.

The Y-axis is tangent to the ellipse at O.

The X-axis is the cross product of Y-axis and the Z-axis.

FIG. 14 illustrates amodel 1300 for which an AMPB has been generated.

After an AMPB has been generated for at least two models (e.g., atracking model and a planning model), the models can be roughly matchedby superimposing their AMPBs onto one another. (Step 810). Given theAMPB of a tracking model as a transform (R_(t), T_(t)) and the AMPB of aplanning model as a transform (R_(p), T_(p)), the transformation of thetracking model to the planning model can be defined as (R_(m), T_(m)),where:R _(m) =R _(p) ·R _(t) ⁻¹  (13)T _(m) =T _(p) −R _(m) ·T _(t) =T _(p) −R _(p) ·R _(t) ⁻¹ ·T _(t)  (14)

Fine Matching Models

After two models (e.g., a tracking model and a planning model) areroughly aligned with one another, the two models can be finely alignedwith one another and a best match stage can be found (Step 404B). In anexemplary embodiment of the present invention, ICP, as previouslydescribed, can be used to finely align the models using vertices of themodels as source points for the ICP algorithm. In the case of usingvertices of a planning model, in accordance with an embodiment of thepresent invention, the vertices only include vertices of a crown part ofthe teeth. Other parts, including root and interproximal areas of theteeth, can be inferred from the crown part and may be modified by anoperator. Also, root areas of the teeth are not normally capture bytracking model. Therefore, in an exemplary embodiment, tracking andplanning models may be matched using only crown vertices.

In an embodiment of the present invention, a plurality of planningmodels can be provided. If treatment is performed in accordance with theInvisalign® System, at least theoretically, the tracking model shouldfit one of the plurality of planning models. This one planning model canbe referred to as the “best matching stage.” To find this “best matchingstage,” matching between the tracking model and each of the plurality ofplanning models can be performed. Various techniques can then beemployed to determine and compare the quality of the matches so as todetermine which of the plurality of planning stages the tracking modelhas a closest match with. For example, the ratio of the matched vertices(i.e., the vertices that are not outliers) to the total number ofvertices can be used to find the best match stage.

Fine Matching Individual Teeth

After fine matching of models is performed and a best match stage isfound, each individual tooth of the planning model corresponding to thebest matching stage (or of the only planning model in the case thatthere is only one planning model) can be matched to the individual teethof the tracking model (Step 404C). Since the two models should alreadybe well aligned due to the previous rough and fine alignment steps, eachtooth in the tracking model should already be close to its correctposition. As previously described, the matching of individual teeth canbe performed using matching algorithms such as surface matching, featurematching, and the like. In an exemplary embodiment, ICP is used to matchthe finely teeth of the models to one another, where teeth vertexes areused by the ICP algorithm.

After tooth matching, teeth are repositioned to the tracking model. Thetooth position in the tracking model is then computed (Step 404C).Basically, a purpose of matching algorithm (rough matching and ICPmatching) is to compute the transformation (movement) between two model.So, in step 404C, the tooth is moved from it's original position inplanning model into position in the tracking model.

According to an embodiment of the present invention, the quality oftooth matching can be evaluated. To evaluate the quality of toothmatching, two matching ratios for each tooth can be defined. A “bestmatching ratio” (MR1) can be defined as:

$\begin{matrix}{{{MR}\; 1} = \frac{{{Number}\mspace{14mu}{of}\mspace{14mu}{vertices}\mspace{14mu}{with}\mspace{14mu}{error}} < {0.1\mspace{14mu}{mm}}}{{Total}\mspace{14mu}{vertices}\mspace{14mu}{in}\mspace{14mu}{crown}}} & (15)\end{matrix}$A “good matching ratio” (MR2) can be defined as:

$\begin{matrix}{{{MR}\; 2} = \frac{{{Number}\mspace{14mu}{of}\mspace{14mu}{vertices}\mspace{14mu}{with}\mspace{14mu}{error}} < {0.2\mspace{14mu}{mm}}}{{Total}\mspace{14mu}{vertices}\mspace{14mu}{in}\mspace{14mu}{crown}}} & (16)\end{matrix}$

Usually, the displacement error of a vertex is in the best matchingratio if it is due to random noise, such as that introduced by scanningthe patient's teeth to acquire a model. Error in the good matching ratiomay come from slight model distortion due to digital detailing (DDT)when teeth are segmented in an impression model using, for example,ToothShaper software. Vertices that are not in the good matching ratioare usually due to the presence of erroneous extra material provided in,for example, an impression or attachment.

The tooth matching ratio can also be used to check the quality of animpression. Table 1 illustrates common sources of error for variousmatching ratios.

TABLE 1 MR2 Matching Ratio MRI Matching Ratio (<0.1 mm) (<0.2 mm) 0-0.40.4-0.6 0.6-1.0   0-0.4 Failed matching N/A N/A 0.4-0.6 Bad impressionLow impression N/A quality quality 0.6-1.0 N/A Extra material or Goodimpression attachment and matching

Tooth Movement Measurement by Stationary Teeth

As a result of the matching step 404, the positions of the teeth in thetracking model can be determined. In an embodiment of the presentinvention, these positions can then be used for a final re-alignment ofthe models that takes into consideration intended and/or actual movementof the teeth. Such realignment can subsequently be used to measuremovements in the positions in teeth of a model.

Two models (e.g., a tracking model and a “best match” planning model)can be re-aligned by detecting stationary or near-stationary elements(Step 406). The stationary or near-stationary elements may includeteeth, regions beyond tooth crowns, and the like. In orthodontictreatment, in general, every tooth is moving. So, there is no absolutelystationary tooth. However, from the treatment plan, it is possible tofind the teeth which are not supposed to be moved in accordance with thetreatment plan. These teeth can be considered to be stationary and canthus be used as reference for measurements of other teeth movement.Accordingly, re-alignment of the models can be performed by minimizingthe cost function of the weighted displacement error between the plannedjaw position (i.e., planning model or treatment model) and achieved jawposition (i.e., tracking model), the cost function being defined as:

$\begin{matrix}{J = {\sum\limits_{i = 1}^{N}{\sum\limits_{j = 1}^{M}{{w_{i} \cdot \left( {{R^{s}\left( {{R_{i}^{P}P_{i,j}} + T_{i}^{P}} \right)} + T^{s} - \left( {{R_{i}^{t}P_{i,j}} + T_{i}^{t}} \right)} \right.^{2}}}}}} & (17)\end{matrix}$

Where, P_(i,j) is the position of vertex j in tooth i; (R_(i) ^(t),T_(i) ^(t)) is the position of the teeth in the tracking model; (R_(i)^(p), T_(i) ^(P)) is the position of the teeth in the planning model;(R^(s), T^(s)) is the relative position of stationary teeth; N is thetotal number of teeth in the models; and M is the total number ofvertexes for each tooth in the models.

In an embodiment of the present invention, the weight w_(i) of eachtooth i can be determined based on the planned tooth movement for acertain stage. Less moved tooth should be more stationary and withbigger weight. The weight for tooth with large movement should be smallor equal 0. In accordance with this embodiment, first, for each vertexin the crown, the following move distances are computed:

Rotation distance RD. For a vertex in the tooth, the displacement vectoris defined as the vector of the vertex from tooth initial position tothe planning position. This displacement vector is projected on theplane perpendicular to the Z-axis and then onto the line perpendicularto the radius; i.e., the rotation distance around the Z axis of tooth(or the incisal-gingival direction).

Tip distance TD, is defined as the movement perpendicular to the vectorfrom the vertex to the root centre in the plane of this vector and theZ-axis.

Intrusion distance ID and extrusion distance ED, the outward and inwardmovement from/to the root in the Z-direction, respectively.

FIG. 15 illustrates a tooth 1400 and an associated vertex 1402, theassociated root 1404, and the relationship between the vertex 1402, root1404, RD, TD, and ID, where ED is in a direction opposite the directionof ID.

The maximum of RD, TD, ID and ED (i.e., “Max_RD”, “Max_TD”, etc.) can befound over all of the vertices in the crown and the weighted sum of themaximal distances (“WMD”) can be computed according to the formula:WMD=w ₁Max_RD+w ₂Max_TD+w ₃Max_ID+w ₄Max_ED  (18)

Where w₁-w₄ are weights that are different for different types of teethand are based on the difficulty of each type of movement and tooth size.For molar and premolar, all movement are difficult, so the weights arebigger. For canine, the extrusion and rotation movements are difficult,so w₁, w₄ are bigger. In an embodiment of the present invention, the WMDcan be limited to be between 0.1 and 2.

Using the WMD, the weight of one tooth movement can be computed as:w=0.1042105/WMD−0.042105  (19)So that when WMD=0.1, w=1; when WMD=2, w=0.01. i.e., if tooth movementis bigger, the weight is almost 0.

In accordance with using equation (19) to calculate the weight of eachtooth, for WMD=2.0, or maximum movement, the weight w will be 0.01; forWMD=0.1, or almost no movement, w=1.0; which means that teeth planned tomove slower contribute more in equation (17) and teeth planned to movefaster contribute less to equation (17). Accordingly, the stationaryposition (R^(s), T^(s)) depends more on slowly moving teeth than onfaster moving teeth. Accordingly, stationary (and near stationary) teethcan be detected.

In another embodiment of the present invention, the weight w_(i) of eachtooth i can be determined based on the de facto immobility of the teeth,since actual movement of teeth may be very different from plannedmovements. Consequently, information regarding which teeth arestationary (or nearly stationary) may be inferred only by comparing thetracking model with the planning models. Accordingly, one method forcalculating the weight of each tooth includes:

1. Assigning the weights for all teeth to 1.

2. For every pair of teeth T1 and T2 in an original or previous trackingmodel, computing a transformation L_(init).

3. For every pair of teeth T1 and T2 in a most recent or currenttracking model, computing a transformation L_(curr).

4. For every vertex v of tooth T1 compute the distance D_(v) betweenL_(init)(v) and L_(curr)(v), i.e., compute the difference between theresults of application of the transformations L_(init) and L_(curr) tothe vertex v.

5. Determining the maximum number D of all numbers D_(v); i.e.,determine the maximum D over all vertices of tooth T1.

6. If D is less than a predefined tolerance, ε, then increasing theweight for tooth T1 by 1. A preferred value for ε is 0.2 mm.

7. Repeating steps 2 to 6 for all pairs of teeth in the same model.

8. Dividing the weight of each tooth by the sum of all weights of theteeth in the same model.

This method automatically assigns bigger weights to the teeth that movethe least amount, thus advantageously detecting stationary (and nearstationary) teeth.

In an embodiment of the present invention, the resulting weightsassigned to equation (17) can be the average of the weights derived byequation (19) and the weights derived according to the aforementionedmethod steps 1 to 8.

Once the tracking model and a planning model are re-aligned based onstationary and/or near stationary elements, planned tooth positions canbe compared with actually achieved tooth positions (Step 408) so as todetect one or more positional differences between the actual and plannedarrangements of the patient's teeth. Such a comparison can includebuilding up an occlusal plane and archform as a measurement reference(Step 408A) and computing tooth movements relative to this measurementreference (Step 408B). Using an occlusal plane and archform formed froma model that has been re-aligned based on stationary and/or nearstationary elements advantageously assures an accurate measurement ofpositional differences.

In orthodontics, the archform is a smooth curve that roughly passesthrough some feature points of a dental arch. It describes the archshape and is important for tooth movement measurement. For example, themesial-distal movement is the movement in a direction tangent to thearchform. The occlusal plane defines the direction ofintrusion-extrusion movement of a tooth.

In an embodiment of the present invention, an archform can beconstructed (Step 408A) as a curve based on any of the points on theteeth in a model. In a preferred embodiment, the archform is constructedas a two-segment cubic curve using the facial axis points of all teethin the tracking model. Similarly, the occlusal plane can be constructed(Step 408A) based on any of the points on the teeth in a model. In apreferred embodiment, the occlusal plane is built by best fitting aplane from the crown centers of all teeth in the tracking model. FIG. 16illustrates a model 1500 for which an archform 1502 has been constructedas a two-segment cubic curve using the facial axis points of all of theteeth in the model 1500.

After the archform and occlusal plane are constructed, an archform basiscan be constructed for each tooth for subsequent calculation of toothmovements. The archform basis can be constructed in accordance with thefollowing definition:

-   -   The origin (O) of the basis is the closest point on the archform        to the centre of the crown.    -   The Z-axis is normal to the occlusal plane.    -   The Y-axis is the tangent to the archform that is projected onto        the occlusal plane.

FIG. 17 illustrates a model 1600 for which an archform basis for a crowncenter 1602 has been constructed.

Once the archform basis is constructed, the tooth movement can becomputed relative to this basis (Step 408B). In an embodiment of thepresent invention, the tooth movement can be computed via translationmovements and rotation parameters. For example, the tooth movement Mwith respect to an archform basis can be computed as:M=[R ^(b)]⁻¹ R _(i) P+T _(i)−(R ₀ P+T ₀))  (20)

Where P is the position of a vertex in the tooth of the treatment model,(R₀, T₀) is the tooth position at an initial stage (e.g., an original orprevious tracking model), (R_(i), T_(i)) is the tooth position at acurrent stage (e.g., a most recent or current tracking model), and(R^(b), T^(b)) is the transform representing archform basis.

In an embodiment of the present invention, equation (20) can be used tocompute the movement of a crown center and root center. In an embodimentof the present invention, the rotation movement of a tooth can bedecomposed into inclination, angulation and rotation, or the rotationangle around Y axis, X axis and Z axis by Euler decomposition method. Inan embodiment of the present invention, for each planning model, theplanned movement and achieved movements are computed based on theplanned tooth positions from the planning models and the achieved toothpositions from the tracking model.

In an embodiment of the present invention, the measurement results,including matching quality, can be output. The output can be used forfuture applications, like date analysis, treatment monitor. The outputcan be provided in XML format, for example. FIG. 18 illustrates an XMLoutput 1700 in accordance with an embodiment of the present invention.

Utilize Partial Surface as Alignment Reference

In order to evaluate the outcome of a treatment, two models can first bealigned with one another. After the alignment, tooth movements can becompared with their initial positions, and the deviation between plannedtooth positions and achieved tooth positions can be calculated.Theoretically, the planned static teeth can be utilized as thereferences for the model alignment. However, in the actual treatment, itis possible that all of the teeth are planned to be moved. It is alsopossible that although some teeth are not planned to be moved, they arenonetheless moved during the actual treatment. For example, unplannedmovement may result from the aligners being worn since the specificinteraction between the aligners and the teeth may be unknown. After thealigners are worn on the teeth, each individual tooth's movement may beunpredictable. Consequently, teeth that are planned to not move may inreality actually be moved. So, in order to more accurately evaluate theabsolute deviation, a static reference can be utilized for aligning twomodels.

In accordance with an embodiment of the present invention, partialregions beyond the tooth crown are used as references to align at leasttwo models; for example, a tracking model and a planning model. When adoctor takes an impression from the patients teeth (or acquires adigital model of the patients teeth using other methods previouslydescribed, such as scan techniques), not only are the teeth crowns shapecaptured, but also the whole arch shape, including gingiva shape,palatine rugae, hard plate, and so forth, are captured. These regionsare all located beyond the teeth crowns. The static region can belocated in any or all of these regions.

FIG. 19 illustrates the general flow of an exemplary process 1800 foraligning two models using a partial region located beyond teeth crowns.

The process 1800 for aligning two models may be used independently ofthe process 400. As an initial step, two models are received by orloaded into a system for automatic alignment (Step 1802). The two modelsmay include a tracking model and a planning model as previouslydescribed. In an exemplary embodiment, the tracking model may be athree-dimensional digital model of a patient's teeth during treatment,and the planning model may be a three-dimensional digital model of thepatient's initial teeth arrangement. These models may be acquired usingany of the techniques previously described.

After loading the tracking and planning models, an alignment step isperformed to align stationary elements of each of the two models withone other (Step 1804). The alignment step 1804 can include automaticallydetecting a partial region of each of the tracking and planning models(1804A), calculating an alignment transform using the detected partialregions (Step 1804B), and aligning the models using the calculatedalignment transform (Step 1804C).

The partial region automatically detected in step 1804A could be on thelingual side or buccal side of teeth included in the models. For anupper jaw, the lingual side is preferred over the buccal side since thelingual side comprises the palatine rugae, hard plate, and gingivalshape. To utilize the partial region beyond tooth crown as an alignmentreference, the partial region need to been automatically detected. Inaccordance with an embodiment of the present invention, the steps fordetecting the partial region may include:

(1) Calculating each tooth's lingual cementoenamel junction (CEJ) point

(2) Connecting the CEJ points in sequence to form a polygon

(3) Filtering out the faces which are outside of the polygon

(4) After filtering, form the partial region by combining the remainingfaces

FIG. 20 illustrates a model 1900 for detecting partial regions. Themodel 1900 includes CEJ points 1902 that have been detected andconnected to form a polygon 1904. Faces 1906 are provided outside of thepolygon 1904, whereas faces 1908 are provided inside of the polygon1904. The region inside the polygon including the faces 1908 is thepotential static region; this region is assumed to comprise at least onestatic part.

To calculate the alignment transform, ICP algorithm may be utilized,which has been described previously in “Iterative Closest PointAlgorithm”. In the implementation, the matching points should be locatedon the partial surfaces of the planned model and tracking model. Byminimizing the error metric in the ICP algorithm, a rigid body transformis obtained as the alignment transform. Then apply the alignmenttransform to one of the models and make that model moved to thealignment position.

Alternatively, the process 1800 for aligning two models may be usedwithin the process 400. For example, the alignment step 1804 could beused in place of the re-alignment step 406. In this case, the step ofloading the tracking and planning models (Step 1802) is unnecessarysince this is performed in step 402. Similarly, the step of computingtooth movements (Step 1806) is unnecessary since this is performed instep 408. By aligning two models using a partial region beyond toothcrowns, a static region can be captured. Advantageously, thestatic/absolute partial region can be captured, the static region can beutilized to align two models, and the tooth movements and the deviation(planned vs. actual) can be quantified in a absolute way.

Experimental Results

To test and evaluate the methods of the present invention, 356 middlecourse correction (MCC) cases were collected and processed. Each casesinclude one treatment model and one tracking model. Among the 356 cases,there were 297 lower jaws, 336 upper jaws and a total of 8751 teeth.

FIG. 21 illustrates a histogram 2000 of the matching quality for allteeth. 95% of the teeth are in good matching, and over 50% of the teethare in best matching. The matching ratios for each are provided on thex-axis, and the percentage of teeth satisfying those matching ratios isprovided on the y-axis.

FIG. 22A illustrates a histogram 2100 of the number of teeth havingmatching ratios for individual teeth numbers in the upper jaw. The toothnumber I provided on the x-axis, where 1, 2, 3 and 14, 15, 16 aremolars, 4, 5, 12, 13 are premolars, 6 and 11 are canines, 7-10 areincisors. The number of teeth in each matching ratio is provided on they-axis. Similarly, FIG. 22 b illustrates a histogram 2110 of the numberof teeth having matching ratios for individual teeth numbers in thelower jaw

FIG. 23A illustrates a graph 2200 showing the mesial-distal movementdistribution of the root centers of molars. The planned movement is onthe x-axis (mm) and the real movement is on the y-axis (mm). FIG. 23Billustrates a graph 2210 similarly showing the medial-distal movementfor crown centers of molars.

The inventors of the subject application recognized that distal movementof tooth roots is difficult to achieve and less predictable than distalmovement of crowns. On average, only 75% of planned movements can beachieved for all kinds of movement. They also recognized that crownmovement is more predictable than distance movement and up to 90% ofplanned movements can be achieved, and that large mesial movements arevery unpredictable and only 50% of planned movements can be achieved.

While the timing of the progress tracking steps described herein can beselected by the practitioner, typically at least general timing forconducting progress tracking measures of the present invention will beincorporated into the treatment plan and, therefore, will be pre-plannedor planned at about the beginning of treatment or early on in the courseof the patient's treatment (e.g., prior to the patient wearing a givenset of appliances so as to reposition the teeth). Thus, in oneembodiment of the invention, a treatment plan will include a prescribedtiming for the planned tracking steps. The prescribed timing can includea specifically recommended date or may include a general increment oftime (e.g., at treatment week 9, 10, 11, etc.), or can be based on thetiming of other events of the treatment plan (e.g., after a patientwears a set of appliances).

Timing of progress tracking steps can be selected to occur based on asomewhat standardized treatment protocol or can be more particularlycustomized to an individual patient. More standardized protocols cantake into account certain population statistics, generalized clinicalexpectations, and/or physiological parameters that can be used togenerally predict rate of movement of a patient's teeth and the minimumlength of treatment time necessary for the patient's teeth to progressoff track if such progression is occurring. Clinical parameters caninclude, for example, root structure, including length, shape, andpositioning, as well as certain jaw characteristics such as jaw bonedensity, patient age, gender, ethnicity, medications/health historyprofile, dental history including prior treatment with orthodontics,type of orthodontic treatment plan (extraction vs. non-extraction), andthe like. Assuming a 2-week wear interval for each appliance, with amaximum tooth velocity of 0.25 mm/tooth per aligner, typically about 16to 20 weeks of repositioning treatment (8 to 10 appliances) is requiredbefore movement of the teeth is substantial enough to detect anon-compliant or off track movement of the teeth, if such off trackmovement is occurring, though more drastic movements can produce offtrack movement after only a few weeks.

As set forth above, timing of tracking measures can be selected based onthe particular movement(s) prescribed and/or characteristics of thepatient being treated and, therefore, are said to be customized to theparticular patient. For example, certain desired tooth movements in atreatment plan may be deemed either more unpredictable or at increasedrisk of moving off track and may require specifically timed tracking ormonitoring. For example, for certain movements including, e.g.,extrusions or rotations of round teeth (e.g., canines), more specific orfrequent tracking may be desired. Additionally, certain physiological orclinical characteristics of the patient may be identified as indicatingthat particularly timed and/or frequency of tracking might be desired.Whether tracking is selected based on standardized protocols or morecustomized to the individual patient, tracking may or may not beselected to uniformly timed during the course of treatment. For example,a lower frequency of tracking measures may be desired or needed duringcertain portions or phases of treatment than others (e.g., spaceclosure). Regardless of whether tracking timing is customized or morestandardized, the selected timing will typically provide the additionaladvantage of efficiently planning tracking in the treatment plan tominimize unnecessary use of practitioner time and other resources.

Once a determination is made that the patient's actual arrangement ofteeth deviates from a planned arrangement and that the patient's teethare not progressing as expected/planned, a change or correction in thecourse of treatment can be selected, for example, by generating arevised or modified treatment plan. Referring to FIGS. 24A-24C, revisedtreatment following determination that a patient's teeth are notprogressing on track is described. As set forth above, a treatment planincludes a plurality of planned successive tooth arrangements for movingteeth along a treatment path from an initial arrangement to a selectedfinal arrangement. The treatment plan, administration of sets ofappliances to a patient according to the planned arrangements, caninclude a plurality of phases (1 through 4) where at time=0, the initialtreatment plan begins. The initial treatment plan is illustrated by asolid line. Matching for a determination of whether a case isprogressing “on track” or “off track”, as described above (e.g., FIG.3), can take place at one or more of the phases or points along theadministration of treatment.

In particular, current tooth positions of the patient can be obtainedfrom the patient at any one or more phases and compared to segmentedmodels of the patient's teeth according to an earlier or originaltreatment plan. Where teeth are determined to be deviating from theplanned treatment plan or progressing “off track”, as illustrated bybroken lines, modification or revision of treatment plan can occur. Inone embodiment, a revised treatment plan can include restaging thepatient's treatment from the determined actual position to theoriginally determined final position (FIG. 24A). Revised treatment path(illustrated by dashed lines) can proceed directly toward the initiallydetermined final position and need not attempt to redirect treatmentback onto the original treatment path. In this case, while partialoverlap/intersection of the revised treatment path with the originaltreatment path may occur, the revised treatment path will at leastpartially diverge from the initial treatment path and proceed directlytoward the initially determined final arrangement of the teeth. Such anapproach may be selected, for example, where retaining the initiallydetermined final position is desired. This approach also advantageouslypermits use of the originally processed and segmented data, therebyallowing avoidance of costly processing steps.

Alternatively, a revised treatment plan can include a more direct“mid-course correction”, in which the revised treatment plan includes amore direct path back toward the a planned arrangement of the initialtreatment plan, as illustrated in FIG. 24B. While this approach may makeuse of the originally planned final arrangement, the more primaryconcern in this example type of correction is redirecting treatment backto the original treatment path, rather than from the actual position andmore directly toward the original final position. In yet anotherembodiment, as illustrated in FIG. 9C, a revised treatment plan caninclude essentially “re-starting” treatment, and generating a new finalarrangement of the teeth, for example, from segmenting and staging a newimpression of the teeth, and directing the patient's teeth from theactual arrangement to the newly determined final arrangement of theteeth.

FIG. 25 is a simplified block diagram of a data processing system 2400that may be used in executing methods and processes described herein.The data processing system 2400 typically includes at least oneprocessor 2402 that communicates with a number of peripheral devices viabus subsystem 2404. These peripheral devices typically include a storagesubsystem 2406 (memory subsystem 2408 and file storage subsystem 2414),a set of user interface input and output devices 2418, and an interfaceto outside networks 2416, including the public switched telephonenetwork. This interface is shown schematically as “Modems and NetworkInterface” block 2416, and is coupled to corresponding interface devicesin other data processing systems via communication network interface2424. Data processing system 2400 can include, for example, one or morecomputers, such as a personal computer, workstation, mainframe, and thelike.

The user interface input devices 2418 are not limited to any particulardevice, and can typically include, for example, a keyboard, pointingdevice, mouse, scanner, interactive displays, etc. Similarly, varioususer interface output devices can be employed in a system of theinvention, and can include, for example, one or more of a printer,display (e.g., visual, non-visual) system/subsystem, controller,projection device, audio output, and the like.

Storage subsystem 2406 maintains the basic required programming,including computer readable media having instructions (e.g., operatinginstructions, etc.), and data constructs. The program modules discussedherein are typically stored in storage subsystem 2406. Storage subsystem2406 typically comprises memory subsystem 2408 and file storagesubsystem 2414. Memory subsystem 2408 typically includes a number ofmemories (e.g., RAM 2410, ROM 2412, etc.) including computer readablememory for storage of fixed instructions, instructions and data duringprogram execution, basic input/output system, etc. File storagesubsystem 2414 provides persistent (non-volatile) storage for programand data files, and can include one or more removable or fixed drives ormedia, hard disk, floppy disk, CD-ROM, DVD, optical drives, and thelike. One or more of the storage systems, drives, etc may be located ata remote location, such coupled via a server on a network or via theInternet's World Wide Web. In this context, the term “bus subsystem” isused generically so as to include any mechanism for letting the variouscomponents and subsystems communicate with each other as intended andcan include a variety of suitable components/systems that would be knownor recognized as suitable for use therein. It will be recognized thatvarious components of the system can be, but need not necessarily be atthe same physical location, but could be connected via variouslocal-area or wide-area network media, transmission systems, etc.

Scanner 2420 includes any means for obtaining an image of a patient'steeth (e.g., from casts 2421), some of which have been described hereinabove, which can be obtained either from the patient or from treatingprofessional, such as an orthodontist, and includes means of providingthe image data/information to data processing system 2400 for furtherprocessing. In some embodiments, scanner 2420 may be located at alocation remote with respect to other components of the system and cancommunicate image data and/or information to data processing system2400, for example, via a network interface 2424. Fabrication system 2422fabricates dental appliances 2423 based on a treatment plan, includingdata set information received from data processing system 2400.Fabrication machine 2422 can, for example, be located at a remotelocation and receive data set information from data processing system2400 via network interface 2424.

It is understood that the examples and embodiments described herein arefor illustrative purposes and that various modifications or changes inlight thereof will be suggested to persons skilled in the art and are tobe included within the spirit and purview of this application and thescope of the appended claims. Numerous different combinations arepossible, and such combinations are considered to be part of the presentinvention.

What is claimed is:
 1. A computer-implemented method for the detectionof deviations from an orthodontic treatment plan, comprising: receivinga tracking model comprising a non-segmented digital representation of anactual arrangement of a patient's teeth after an orthodontic treatmentplan has begun for the patient for comparison to a previously segmentedplan model comprising a segmented digital representation of apre-determined planned arrangement of the patient's teeth; performing afirst alignment of the non-segmented digital representation of theactual arrangement and the segmented digital representation of thepre-determined planned arrangement such that teeth in the segmenteddigital representation of the pre-determined planned arrangement arepositioned to substantially match corresponding tooth positions in thenon-segmented digital representation of the actual arrangement, thefirst alignment comprising: a rough matching comprising automaticallydetecting a structural feature from the non-segmented digitalrepresentation of the actual arrangement previously unidentified in thetracking model and a structural feature from the segmented digitalrepresentation of the pre-determined planned arrangement, and roughaligning the non-segmented digital representation of the the actualarrangement and the segmented digital representation of thepre-determined planned arrangement based on the detected structuralfeatures; and a fine aligning of the non-segmented digitalrepresentation of the actual arrangement and the segmented digitalrepresentation of the pre-determined planned arrangement, the finealigning comprising matching a surface of the non-segmented digitalrepresentation of the actual arrangement and a surface of the segmenteddigital representation of the pre-determined planned arrangement;performing a second alignment of the non-segmented digitalrepresentation of the actual arrangement and the segmented digitalrepresentation of the pre-determined planned arrangement, comprising:comparing the non-segmented digital representation of the actualarrangement with the segmented digital representation of thepre-determined planned arrangement so as to detect stationary elementsof the patient's dentition such that positions of one or morenon-stationary teeth are measurable relative to the detected stationaryelements, and re-aligning the non-segmented digital representation ofthe actual arrangement and the segmented digital representation of thepre-determined planned arrangement based on the detected stationaryelements; and detecting, based on the non-segmented digitalrepresentation of the actual arrangement and the segmented digitalrepresentation of the pre-determined planned arrangement as aligned perthe second alignment, one or more positional differences between theactual arrangement of the patient's teeth and the pre-determined plannedarrangement of the patient's teeth.
 2. The method of claim 1, whereinthe non-segmented digital representation of the actual arrangement iscreated from scanning the patient's teeth or an impression thereof. 3.The method of claim 1, wherein the orthodontic treatment plan comprisesa plurality of planned successive tooth arrangements for moving teethalong a treatment path from an initial arrangement to a selected finalarrangement.
 4. The method of claim 1, wherein the segmented digitalrepresentation of the pre-determined planned arrangement comprises amodel of the teeth in an initial arrangement, an intermediatearrangement, or a final arrangement.
 5. The method of claim 1, whereinthe automatically detecting a structural feature comprises constructinga buccal ridge ellipse and an anterior middle point basis for each ofthe non-segmented digital representation of the actual arrangement andthe segmented digital representation of the pre-determined plannedarrangement, and the rough aligning comprises roughly aligning thenon-segmented digital representation of the actual arrangement and thesegmented digital representation of the pre-determined plannedarrangement by superimposing respective anterior middle point bases. 6.The method of claim 1, wherein the matching a surface of thenon-segmented digital representation of the actual arrangement and asurface of the segmented digital representation of the pre-determinedplanned arrangement comprises using a 3-dimensional model (3D)registration algorithm to align individual teeth of the segmenteddigital representation of the pre-determined planned arrangement withcorresponding teeth of the non-segmented digital representation of theactual arrangement.
 7. The method of claim 6, wherein the 3D modelregistration algorithm comprises an iterative closest point algorithm.8. The method of claim 1, further comprising assessing tooth matchingquality following the fine aligning.
 9. The method of claim 1, whereinthe stationary elements comprise teeth expected to remain stationaryaccording to the treatment plan.
 10. The method of claim 1, wherein eachof the stationary elements comprise a partial region beyond a toothcrown.
 11. The method of claim 1, wherein said re-aligning thenon-segmented digital representation of the actual arrangement and thesegmented digital representation of the pre-determined plannedarrangement comprises optimizing a square distance of vertices in thenon-segmented digital representation of the actual arrangement and thesegmented digital representation of the pre-determined plannedarrangement, the vertices being weighted according to a probability ofthe vertices being stationary.
 12. The method of claim 1, wherein thedetecting one or more positional differences comprises measuringmovement of a non-stationary tooth relative to a stationary element. 13.The method of claim 1, further comprising constructing archform andocclusal planes as orthodontic references for measuring movement ofteeth.
 14. The method of claim 1, wherein the detecting one or morepositional differences comprises measuring tooth movement byconstructing archform and occlusal planes, constructing an archformbasis for a tooth, and computing movement of the tooth relative to thecorresponding archform basis.
 15. The method of claim 1, wherein adetected one or more positional differences indicates that the patient'sprogression through the treatment plan is off track.
 16. Acomputer-implemented method of managing delivery and patient progressionthrough an orthodontic treatment plan, comprising: providing an initialtreatment plan for a patient, the initial treatment plan comprising aplurality of planned successive tooth arrangements for moving teethalong a treatment path; providing a plurality of orthodontic appliancesfor successively moving the patient's teeth at least partially along thetreatment path, the plurality of orthodontic appliances being shaped toreceive the patient's teeth; and tracking progression of the patient'steeth along the treatment path, the tracking comprising: receiving anon-segmented tracking model comprising a non-segmented digitalrepresentation of an actual arrangement of the patient's teeth followingadministration of the plurality of orthodontic appliances for comparisonto a previously segmented plan model comprising a segmented digitalrepresentation of a pre-determined planned arrangement of the patient'steeth; performing a first alignment of the non-segmented digitalrepresentation of the actual arrangement and the segmented digitalrepresentation of the pre-determined planned arrangement such that teethin the segmented digital representation of the pre-determined plannedarrangement are positioned to substantially match corresponding toothpositions in the non-segmented digital representation of the actualarrangement; performing a second alignment of the non-segmented digitalrepresentation of the actual arrangement and the segmented digitalrepresentation of the pre-determined planned arrangement comprising:comparing the non-segmented digital representation of the actualarrangement with the segmented digital representation of thepre-determined planned arrangement so as to detect stationary elementsof the patient's dentition such that positions of one or morenon-stationary teeth are measurable relative to the detected stationaryelements, and re-aligning the non-segmented digital representation ofthe actual arrangement and the segmented digital representation of thepre-determined planned arrangement based on the detected stationaryelements; and detecting, based on the non-segmented digitalrepresentation of the actual arrangement and the segmented digitalrepresentation of the pre-determined planned arrangement as aligned perthe second alignment, one or more positional differences between theactual arrangement of the patient's teeth and the pre-determined plannedarrangement of the patient's teeth, the detecting comprisingconstructing a measurement reference including an occlusal plane and/orarchform, and computing tooth positions in the tracking and/or planmodels relative to the measurement reference.
 17. The method of claim16, wherein the initial treatment plan further comprises a prescribedtiming for the tracking.
 18. The method of claim 17, wherein theprescribed timing for the tracking is customized to the patient.
 19. Themethod of claim 16, further comprising generating a revised treatmentplan in response to the actual tooth arrangement deviating from theplanned tooth arrangement.
 20. The method of claim 19, wherein therevised treatment plan comprises a plurality of successive tootharrangements to move the patient's teeth along a revised treatment pathfrom their actual position directly toward the pre-determined plannedarrangement or a revised final tooth position.
 21. The method of claim20, wherein the revised treatment plan comprises a mid-coursecorrection.
 22. A system for detecting deviations from an orthodontictreatment plan, the system comprising a computer having a processor anda computer readable medium, the computer readable medium comprisinginstructions that when executed cause the computer to: receive atracking model comprising a non-segmented digital representation of anactual arrangement of a patient's teeth after an orthodontic treatmentplan has begun for the patient for comparison to a plan model comprisinga segmented digital representation of a pre-determined plannedarrangement of the patient's teeth; perform a first alignment of thenon-segmented digital representation of the actual arrangement and thesegmented digital representation of the pre-determined plannedarrangement such that teeth in the segmented digital representation ofthe pre-determined planned arrangement are aligned to substantiallymatch corresponding tooth positions in the non-segmented digitalrepresentation of the actual arrangement, the first alignmentcomprising: a rough matching comprising automatically detecting astructural feature from the non-segmented digital representation of theactual arrangement previously unidentified in the tracking model and astructural feature from the segmented digital representation of thepre-determined planned arrangement, and rough aligning the non-segmenteddigital representation of the actual arrangement and the segmenteddigital representation of the pre-determined planned arrangement basedon the detected structural features; and a fine aligning of thenon-segmented digital representation of the actual arrangement and thesegmented digital representation of the pre-determined plannedarrangement comprising matching a surface of the non-segmented digitalrepresentation of the actual arrangement and a surface of the segmenteddigital representation of the pre-determined planned arrangement;perform a second alignment of the non-segmented digital representationof the actual arrangement and the segmented digital representation ofthe pre-determined planned arrangement, the second alignment comprising:comparing the non-segmented digital representation of the actualarrangement with the segmented digital representation of thepre-determined planned arrangement so as to detect stationary elementsof the patient's dentition such that positions of one or morenon-stationary teeth are measurable relative to the detected stationaryelements, and re-aligning the non-segmented digital representation ofthe actual arrangement and the segmented digital representation of thepre-determined planned arrangement based on the detected stationaryelements; and detect, based on the non-segmented digital representationof the actual arrangement and the segmented digital representation ofthe pre-determined planned arrangement as aligned per the secondalignment, one or more positional differences between the actualarrangement of the patient's teeth and the pre-determined plannedarrangement of the patient's teeth, the detecting comprisingconstructing a measurement reference including an occlusal plane and/orarchform, and computing tooth positions in the tracking and/or planmodels relative to the measurement reference.
 23. A method for detectingdeviations from an orthodontic treatment plan, comprising: receiving atracking model comprising a digital representation of an actualarrangement of a patient's teeth after an orthodontic treatment plan hasbegun for the patient for comparison to a plan model comprising apre-determined planned arrangement of the patient's teeth; performing analignment between the plan model and the tracking model using a partialregion beyond a tooth crown of the plan model and a partial regionbeyond a tooth crown of the tracking model such that stationary elementsof each of the plan model and the tracking model are aligned with oneanother, the alignment including detecting the partial region of each ofthe tracking model and the plan model based on a polygon formed frompredetermined points on at least some of the teeth in the plan model anda polygon formed from predetermined points on at least some of the teethin the tracking model; and detecting one or more positional differencesbetween the actual arrangement of the patient's teeth and thepre-determined planned arrangement of the patient's teeth.
 24. Themethod of claim 23, wherein the performing an alignment furtherincludes: calculating an alignment transform using the detected partialregions, and aligning the tracking model and the plan model using thecalculated alignment transform.
 25. The method of claim 23, wherein thepartial regions include at least one of a gingiva shape, palatine rugaeand hard plate.
 26. The method of claim 23, wherein the detecting thepartial region of each of the tracking model and the plan modelincludes, for each model: calculating a lingual cementoenamal junction(CEJ) point on each tooth in the model; connecting the cementoenameljunction (CEJ) points in sequence to form the respective polygon;filtering out faces which are outside of the respective polygon; andafter filtering, forming the respective partial region by combiningremaining faces.
 27. A computer-implemented method for the detection ofdeviations from an orthodontic treatment plan, comprising: receiving atracking model comprising a non-segmented digital representation of anactual arrangement of a patient's teeth after an orthodontic treatmentplan has begun for the patient for comparison to a previously segmentedplan model comprising a segmented digital representation of apre-determined planned arrangement of the patient's teeth; performing analignment of the non-segmented digital representation of the actualarrangement and the segmented digital representation of thepre-determined planned arrangement, the alignment comprising: a roughmatching comprising automatically detecting a structural feature fromthe non-segmented digital representation of the actual arrangementpreviously unidentified in the tracking model and a structural featurefrom the segmented digital representation of the pre-determined plannedarrangement, and rough aligning the non-segmented digital representationof the actual arrangement and the segmented digital representation ofthe pre-determined planned arrangement based on the detected structuralfeatures; and a fine aligning of the non-segmented digitalrepresentation of the actual arrangement and the segmented digitalrepresentation of the pre-determined planned arrangement, the finealigning comprising matching a surface of the non-segmented digitalrepresentation of the actual arrangement and a surface of the digitalrepresentation of the pre-determined planned arrangement; and followingthe alignment of the non-segmented digital representation of the actualarrangement and the segmented digital representation of thepre-determined planned arrangement, detecting one or more positionaldifferences between the actual arrangement of the patient's teeth andthe pre-determined planned arrangement of the patient's teeth, thedetecting comprising constructing a measurement reference including anocclusal plane and/or archform, and computing tooth positions, relativeto the measurement reference, in at least one of the group consisting ofthe tracking model and the plan model.